How do you derive the pKa from Ka?

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The pKa can be derived by taking the negative logarithm of Ka so that pKa = minus log(Ka). Ka is known as the acid dissociation constant and is a measure of the strength of the acid. The pKa is the acid disassociation constant on a logarithmic scale, and acids with a pKa below minus 2 are considered strong acids.

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The Ka for most acids is experimentally determined and is a relatively simple calculation, assuming the concentration of the ions and acid in the solution is known. Ka = [H+][A-]/[HA]. In the case of chemistry equations, the square brackets are typically used to denote concentrations. Therefore, [H+] refers to the concentration of hydrogen ions, [A-] refers to the concentration of the conjugate base of the acid, and [HA] refers to the concentration of the total acid. The conjugate base is the negatively charged ion remaining after the hydrogen ion has disassociated from the acid. Therefore, the Ka is a simple ratio between the concentrations of the disassociated parts of the acid, A- and H+, and the total acid, HA.

In almost all cases, the pKa is used to discuss acids, rather than the Ka, because the logarithmic scale of pKa makes it easier to compare. It is also possible to derive the pH of an acid from the pKa as long as the concentrations of the conjugate base and the total acid are known. In the case of monoprotic acids, or acids that can only lose one hydrogen ion, the equation pH = pKa + log [A-]/[HA] is used.